This invention relates to an electronic musical instrument and, more particularly, to a digital type electronic musical instrument capable of producing tone signal waves by calculation under algorithms wherein different set of computations provide different kinds of tone (properties, e.g., different tone colors).
In a prior art electronic musical instrument of a type wherein tone signals (or tone source signals) are produced by implementing a predetermined algorithm, this algorithm is a fixed one and tones of various tone colors are produced by this fixed algorithm. In an electronic musical instrument employing a frequency modulation technology, for example, a basic algorithm is implemented by the following equation (1); EQU e(t)=A(t) sin {n.sub.1 .omega.t+I(t) sin n.sub.2 .omega.t} (1)
where A(t) is a coefficient determining magnitude of the amplitude of a calculated waveform (i.e. envelope amplitude), I(t) is a coefficient determining depth of the modulation (modulation index), n.sub.1 .omega. and n.sub.2 .omega. are angular velocities respectively determining the frequency of the carrier and that of the modulating wave, which angular velocities correspond to the tone pitch of a depressed key.
In this type of electronic musical instrument, algorithm is also implemented by the following equation (2) which is so to speak a multi-series application of the equation (1). ##EQU1## where A.sub.k (t), I.sub.k (t), n.sub.1k .omega., n.sub.2k .omega. are the same as A (t), I(t) n.sub.1 .omega. and n.sub.2 .omega. for every k=1, 2, 3, . . . , m.
The algorithm is also implemented by the following equation (3) which is obtained by turning the equation (1) to polynominal (multi-term fashion): ##EQU2## where A(t), I.sub.k (t), n.sub.1 .omega., n.sub.2k .omega. are the same as the above described values.
The algorithm in this type of electronic musical instrument is also implemented by the following equation (4) which is obtained by nesting the equation (1): EQU e(t)=A(t) sin [n.sub.1 .omega.t+I.sub.1 (t) sin {n.sub.2 .omega.t+I.sub.2 (t) sin n.sub.3 .omega.t}] (4)
in which a subjected to frequency modulation in a double mode. A(t), I.sub.1 (t), I.sub.2 (t), n.sub.1 .omega., n.sub.2 .omega. and n.sub.3 .omega. are the same values as those described above.
Although there have been proposed various devices for producing tones by implementing algorithm described above, each of these devices can carry out only one of the described algorithms, i.e. only a fixed type algorithm peculiar to the device.
It should be noted, however, that harmonic spectra of tone signals obtained by implementation of the above described algorithms are different from one another so that no single one of the algorithms can achieve production of all kinds of tone colors (tone properties). For example, a tone signal produced by implementation of calculation in accordance with the equation (1) is suited for synthesis of certain particular tone colors but not for synthesis of other tone colors. The same is the case with a tone signal produced by implementation of the equation (2), (3) or (4).
Accordingly, the prior art devices which employ a fixed algorithm (i.e. only one kind of algorithm) have limitation in the range of tone color (tone properties) produced by the device with a result that sufficient variety in the tone color can hardly be obtained.